Pleat-and-pinch folding apparatus is known. Usually a reciprocating pleating blade is vertically reciprocated, transverse to the plane of transport of the paper web to push the paper web into the nip between a pair of rollers which rotate against each other and with the same speed. This type of apparatus is frequently used with multiple-layer webs, that is, with webs which have been prefolded in a folding former. A description of such an apparatus is found in the by Alexander Braun "Der Tiefdruck", Frankfurt am Main, 1952, pages 150, 151; 154; 155; 207, 208 ("Gravure Printing"). This arrangement has the disadvantage that the pleat can be applied to the web only when the printed web is stationary. In order to stop a printed web, being ejected or fed from a printing machine, a brake is necessary which usually is formed with a stop or abutment sheet or edge. Braking a moving web of paper at times introduces distortions or twists of the printed web; the abutment can damage the edge of the printed material which is fed thereagainst, particularly if the feed of the printed material is comparatively fast.